Computers for stabilization systems



M I EiAbi-Ufi mm H. M. JAMES COMPUTERS FOR STABILIZATION SYSTEMS Filed Jan. 5, 1946 2 Sheets-Sheet 1 FOLLOW-UP STABLE TR ELEMENT RESOLVER 1. I 39' FOLLOW-UP l I J I 34 4| I I l 1 l INVENTOR HUBERT M. JAMES ATTORNEY Feb. 25, 1958 H. M. JAMES 2,824,693

COMPUTERS FOR STABILIZATION SYSTEMS Filed Jan. 5, 1946 2 Sheets-Sheet 2 ,PERPENDIGULAR TO PLANE OF DECK.

me OF SIGH To TARGET HORIZONTAL PLANE OF SHIP INVENTOR HUBERT M. JAMES ATTORNEY United States Patent COMPUTERS FOR STABILIZATION SYSTEMS Hubert M. James, Belmont, Mass., assignor, by mesne assignments, to the United States of America as represented by the Secretary of the Navy Application January 5, 1946, Serial No. 639,460

6 Claims. (Cl. 235-615) This invention relates to electrical computers and more particularly to apparatus for accurately and rapidly computing level and cross level angles for an object at a first line of sight at a known train angle, when these angles are known for a second line of sight to another object.

There are computers well-known in the art which give approximate solutions of the problem of computing level and cross level angles. This invention provides a computer to solve the exact relations between roll and pitch and level and cross level angles as well as between level and cross level angles for objects at two different lines of sight.

An object of this invention is to provide apparatus for accurately and rapidly furnishing level and cross level angles for an object at a first line of sight at a known train angle when these angles are known for a second line of sight to another object.

Another object is to provide apparatus which furnishes accurately and rapidly the azimuth train and elevation data to a gun, searchlight, radar antenna, or similar directive device when given values of roll, pitch and train angle from a stable element.

Another object is to provide apparatus which furnishes accurately and rapidly azimuth train data to a gun, searchlight, radar antenna, or similar directive device from the train angle of a target as found by a stabilized director.

Another object is to provide apparatus which furnishes accurately and rapidly the level and cross level angles when the pitch, roll and deck train are known.

These and other objects and features of this invention will become apparent upon consideration of the following detailed description when taken together with the accompanying drawings in which:

Fig. 1 is a circuit diagram of one embodiment of this invention.

Fig. 2 is a circuit diagram of the resolver of Fig. 1; and

Fig. 3 is a diagram showing the various angles involved in the use of this invention.

The problem of computing roll and pitch from given values of level and cross level is essentially the same as that of computing level and cross level from roll and pitch, or level and cross level with respect to one line of sight from level and cross level values for another line of sight. For directive devices such as guns, Searchlight, and antennas which are unstabilized, the desired level and cross level angles for laying or controlling the direction of these devices can be computed from data provided by the stable element of a director with fixed or independently changing line of sight. With a stabilized director, data are provided with reference to a stabilized horizontal plane. The data from the stable element must be rapidly converted to a deck train and trunnion elevator order, since unstabilized devices must be laid with reference to the plane of the deck of the ship itself. The apparatus of the present invention gives directly an exact solution.

In Fig. 2 is disclosed a device known as a resolver which is a component of the apparatus of this invention. The

resolver is essentially a two-phase differential synchro, i. e.,

a two-phase transformer with rotatable secondaries or rotors and a one-to-one ratio between each primary and secondary. As shown, rotors 12 and 13 are rotatable about an axis perpendicular to the plane of the paper but their angular position one to the other is fixed so their axes lie degrees apart. Let rotors 12 and 13 be rotated to a position where axis line OO' is at an angle 0 with respect to the horizontal, and let R. M. S. voltages E and E be applied to stator coils 10 and 11 respectively. The R. M. S. voltage outputs of, rotor coils 12 and 13, and designated E and E respectively, will then be:

E =E cos lH-E sin 0 ER2=ES1 Sin 0+ES2 COS 0 Referring to Fig. 3, there is disclosed a diagram of the various angles to be dealth with by the embodiment of Fig. 1. The circle with center 0 in which the diagram is inscribed is a unit circle in the vertical plane. The horizontal diameter of this circle is the projection of a corresponding circle in the horizontal plane. The plane of this last mentioned circle is the previously mentioned stabilized horizontal plane. These two circles determine a spherical surface. Let a ship be considered as located at center 0. The line OT then represents the line of sight from the ship to a target. Point T is on the surface of the sphere determined by the two circles, but the target is not necessarily on this surface. A vertical plane through the fore-and-aft axis of the ship will intersect the unit sphere in a great circle, of which the arc ABC is shown. The length of the arc BC from the horizontal plane to the point of intersection of the fore-and-aft axis is equal to the pitch angle P, since the sphere is a unit sphere. A plane perpendicular to the fore-and-aft axis of the ship will intersect the unit sphere in a great circle, of which the arc EFG is shown. The are FG from the line FO, perpendicular to the fore-and-aft axis, to the horizontal plane is equal to the roll angle R. A vertical plane including the origin and the point T will intersect the unit sphere in a great circle of which ATHJ is an arc. H] has a length equal to the level angle L. A plane perpendicular to the side of the level angle, OJ, will intersect the unit sphere in a great circle of which the arc EKM is shown. The are KM from the deck plane to the horizontal plane is equal to the cross level angle Z. The angle, measured clockwise on the ships deck as seen from above, from the fore-and-aft axis of the ship to the side of the level angle in the ships deck is the train angle a of the target which is equal to the are C].

The exact relations of the angles P, R, L, Z and a are simply derived by application of spherical trigonometry to the spherical triangles appearing in Fig. 3. This gives the equations:

Sin P=sin Z cos L sin u+sin L cos a Tan R=sec Z tan L sin x+tan Z cos a or conversely:

Sin L=-sin R cos P sin u-l-sin P cos a Tan Z=sec R tan P sin a+tan R cos 0c Cos R tan Z=tan P sin a+sin R cos 0c The equivalence of the Equations 4 with the Equations 1 as regards dependence of the expressions on a will be readily apparent.

Referring again to the resolver of Fig. 2, if the inputs to stators 10 and 11 correspond to sin R and tan P and angle becomes the angle on, the outputs from rotor coils 13 and 12 will be (-sin R sin a+tan P cos a) and (tan P sin a-I-sin R cos a) respectively, or the right hand quantities of Equations 4.

In Fig. 1 is shown an embodiment of this invention which provides conventional apparatus including followup systems, similar to the servomechanisms disclosed in my copending application No. 617,l44, filed September 8, 1945, for Compound Resolver Computer, to maintain voltages in balance with the resolver outputs. In maintaining a balance with the voltage outputs from the resolver, the follow-up systems satisfy the equalities of Equations 4 and derive ultimate rotational shaft outputs corresponding to the angles L and Z. Stable element 20 provides shaft rotation outputs proportional to R and P and train angle 0:. Through mechanical linkage 21 the R output of stable element 20 drives slider contacts 22 and 23 of potentiometer 24 having a winding which varies in resistance per unit length in accordance with the sine function in such a way as to pick off between 22 and 23 an alternating voltage proportional to sin R. A source of alternating voltage is provided by generator 25 connected across potentiometer 24. Similarly an alternating voltage proportional to tan P is provided by linkage 28 driving slider contacts 29 and 30 of potentiometer 31 having a winding which varies in resistance per unit length in accordance with the tangent function, across which generator 32, in phase with generator 25, is connected as a voltage source. The voltages sin R and tan P are applied to the stator windings of resolver 33 as shown in Fig. 2. By mechanical linkage 34, stable element 20 positions the rotor of resolver 33 at a train angle a with the ships heading. The electrical outputs of resolver 33 then become (-sin R sin a+tan P cos a) in output circuit 38 and (tan P sin a+sin R cos a) in output circuit 39. These are the right hand quantities of the Equations 4.

Follow-up systems 40 and 41 are responsive to the output voltages of resolver 33 and to voltages derived from potentiometers 42 and 43, respectively, and are actuated by voltage difference to drive output shafts L and Z in a direction to reduce the voltage difference to zero. Potentiometer 42 is so wound that displacement of slider contact 47 by an amount proportional to L will change the voltage between contacts 47 and 48 proportionally to sin L. Moreover, the voltage impressed between the ends of potentiometer 42 is varied proportionally to cos P or sec P, as will be seen. Accordingly, the resultant balancing voltage between contacts 47 and 48 is proportional to (sec P sin L).

In a similar fashion, the displacement of slider contact 49 of potentiometer 43 by an amount proportional to Z changes the voltage between contacts 49 and 50 proportionally to tan Z. But, since the voltage impressed across potentiometer 43 alternates proportionally to cos R, the resultant balancing voltage between contacts 49 and 50 is proportional to (cos R tan Z).

The quantities (sec P sin L) and (cos R tan Z) are the left hand quantities of the Equations 4. By balancing the voltages from resolver 33 against those picked oflf from potentiometers 42 and 43, the follow-up systems 40 and 41 continually solve the Equations 4 and to move to the movable contacts 47 and 49 by displacements proportional to the desired quantities L and Z respectively.

The alternating voltage impressed upon potentiometer 42 is taken between movable contact 51 and end 52 of potentiometer 53. An alternating voltage source 54 in phase with generator 25, is connected across potentiometer 53. Stable element 20, through mechanical linkage 56, drives movable contact 51 in such a way as to pick cos P or sec P. In like manner the alternating voltage impressed upon potentiometer 43 is taken between movable contact 57 and end 58 of potentiometer 59, across which alternating voltage source 60, in phase with generator 25, is connected. Stable element 20, through mechanical linkage 61, drives movable contact 57 so as to pick off between 57 and 58 the alternating voltage proportional to cos R.

The embodiment of the invention shown in Fig. 3 is, therefore, a computer which solves the Equations 4, and when R, P and a are known, it provides data as to L and Z.

It will be noted that when the train angle on between stator and rotor of the resolver of Fig. 3 is zero, the computer output L equals the pitch P and output Z equals the roll R. Thus for a first line of sight at a train angle a, the level angle L and cross level angle Z can be considered to be computed from a second line of sight at train angle a=0 whose level and cross level angles are known. More precisely, all the preceding equations and illustrations remain valid if the following replacements are made: L by L Z by Z P by L R by Z and on by (oi -0L The Equations 4 then become:

Cos Z tan Z =tan L sin (oc a +sin Z cos (11 -01 In other words the computer of this invention can de termine outputs L and Z, for a first line of sight at a train angle oi when L and Z are known for a second line of sight at a train angle (1 Although there is shown and described only a certain specific embodiment of this invention, the many modifications possible thereof will be readily apparent to those skilled in the art. Therefore, this invention is not to be limited except insofar as is necessitated by the prior art and the spirit of the appended claims.

What is claimed is:

1. A computer for the simultaneous solution of equations in the form:

Sec P sin L=sin R sin a+tan P cos a Cos R tan Z=tan P sin u-I-Sill R cos a comprising, means for generating an alternating voltage proportional to sin R, means for generating an alternating voltage proportional to tan P, means for combining and modifying according to an angle a said voltages proportional to sin R and tan P for producing resultant voltages proportional to (-sin R sin u+tan P cos a) and (tan P sin a+sin R cos a), means for generating a voltage proportional to see P, means for generating a voltage proportional to cos R, means for generating a voltage proportional to sin L including a first control element, means for generating a voltage proportional to tan Z including a second control element, a first means for combining said voltages proportional to sec P and sin L for generating a balancing voltage proportional to (see P sin L), and a second means for combining said voltages proportional to cos R and tan Z for generating a balancing voltage proportional to (cos R tan Z), said first and second combining means including follow-up means for matching said resultant voltages and said balancing voltages respectively, said first and second control elements being mechanically coupled to said follow-up means and responsive thereto to control said balancing voltages, the displacements of said control elements being.

proportional to the quantities L and Z respectively.

2. A computer for the simultaneous solution of equations in the form:

Sec P sin L=sin R sin a.+tan P cos a. Cos R tan Z=tan P sin a-l-sin R cos 0.

comprising, a first source of alternating voltage, a first potentiometer connected across said first source, the slider contact of said first potentiometer being adapted to move such that the voltage tapped off is proportional to sin R, a second source of alternating voltage, a second potentiometer connected across said second source, the slider contact of said second potentiometer being adapted to move such that the voltage tapped oif is proportional to tan P, a resolver, whose variable angle between rotors and stators is designated as a, said resolver being adapted to receive said voltages proportional to sin R and tan P and to produce resultant output voltages proportional to (sin R sin a+tan P cos a.) and (tan P sin a+sin R cos a) a third source of alternating voltage, a third potentiometer connected across said third source, the slider contact of said third potentiometer being adapted to move such that the voltage tapped off is proportional to see P, a fourth source of alternating voltage, a fourth potentiometer connected across said fourth source, the slider contact of said fourth potentiometer being adapted to move such that the voltage tapped off is proportional to cos R, a fifth potentiometer adapted to receive across it said voltage proportional to sec P, the slider contact of said fifth potentiometer being adapted to move such that the balancing voltage tapped ofl is proportional to (sec P sin L) a sixth potentiometer adapted to receive across it said voltage proportional to cos R, the slider contact of said sixth potentiometer being adapted to move such that the balancing voltage tapped off is proportional to (cos R tan Z) a first follow-up means adapted to receive said resolver output voltage proportional to (sin R sin +tan P cos a) said first follow-up means being coupled to said slider contact of said fifth potentiometer for moving said slider contact to tap off said balancing voltage proportional to (see P sin L), and a second follow-up means adapted to receive said resolver output voltage proportional to (tan P sin-i-sin R cos a) said second follow-up means being coupled to said slider contact of said sixth potentiometer for moving said slider contact to tap off said balancing voltage proportional to (cos R tan Z), the displacement of said slider contacts being proportional to the quantities L and Z respectively.

3. An electrical computer for automatically solving the spherical trigonometric relationship between roll, pitch, and train angles measured between a stabilized horizontal plane and an unstabilized surface to obtain level and cross-level angular aiming data for unstabilized directive devices mounted on said surface comprising, a source of alternating potentials, means for deriving potentials from said source varying as the sine and cosine of said angle of roll and as the tangent and secant of said angle of pitch, a resolving mechanism energized by said potential representing the sine of the angle of roll and said potential representing the tangent of the angle of pitch and actuated by the measured angle of train to generate resultant voltages proportional to the product of said potentials and said train angle in accordance with said trigonometric relationship, a first potentiometer energized by said potential representing the cosine of said angle of roll and having a moving contact arm adjustable to provide an output voltage proportional to the tangent of its motion, a second potentiometer energized by, said potential representing the secant of said angle of pitch and having a moving contact arm providing an output voltage proportional to the sine of its motion, and motor means actuated in response to said resultant voltages and said first and second potentiometer output voltages to control the motion of said moving contact arms to reduce the difference between said output voltages and said resultant potentials to zero, whereby the motion of said motor means represents the level and cross-level angular motion.

4. An electrical computer for automatically solving equations of the form:

Sec P sin L=sin R sin a+tan P cos a. Cos R tan Z=tan P sin u+sin R cos a.

to obtain level and cross-level aiming data for unstabilized directive devices from roll, pitch and train angles ascertained from a stabilized horizontal plane comprising, a first generator for producing an alternating voltage proportional to sin R, a second generator for producing an alternating voltage proportional to tan P, a resolver energized by said alternating voltages and actuated in accordance with an angle a. for producing resultant voltages proportional to (sin R sin a+tan P cos a) and (tan P sin a+cos R cos a), a third generator for producing an alternating voltage proportional to see P, a fourth generator for producing an alternating voltage proportional to cos R, a first potentiometer energized by the output voltage of said third generator and having a moving contact arm providing an output voltage (sec P sin L) proportional to the sine of its motion, a second potentiometer energized by the output voltage of said fourth generator and having a moving contact arm providing an output voltage cos R tan Z proportional to the tangent of its motion, a follow-up system responsive to said resolver resultant voltages and the output voltages of said first and second otentiometers, respectively, and actuated by the differences therebetween to drive said moving contact arms of said first and second potentiometers so as to reduce said differences to zero, whereby the displacements of said moving arms is proportional to the quantities L and Z, respectively.

5. An electrical computer for automatically solving for level and cross-level angular aiming data for unstabilized directive devices from roll, pitch and train angle measurements made with respect to a stabilized reference horizontal plane comprising, a stable element having a plurality of output shafts providing angular rotation proportional to said pitch, roll and train angles, a source of alternating potentials, a first potentiometer energized by a potential from said source and having a moving contact arm responsive to the angular rotation of an output shaft of said stable element to generate an output voltage proportional to the tangent of said angle of pitch, a second potentiometer energized by a potential from said source and having a moving contact arm responsive to the angular rotation of an output shaft of said stable element to generate an output voltage pro portional to the secant of said angle of pitch, a third potentiometer energized by a potential from said source and having a moving contact arm responsive to the angular rotation of an output shaft of said stable element to generate an output voltage proportional to the sine of said angle of roll, a fourth potentiometer energized by a potential from said source and having a moving contact arm responsive to the angular rotation of an output shaft of said stable element to generate an output voltage proportional to the cosine of said angle of roll, a twophase rotary transformer having a stator wound with two independent windings and a rotor with two windings in quadrature, wherein one stator winding is energized by the output voltage of said first potentiometer and the other stator winding is energized by the output voltage of said third potentiometer, and said rotor is actuated in response to an angular rotation by an output shaft of said stable element providing angular rotation proportional to said train angle to induce resultant potentials in said rotor windings related to said energizing potentials by a function of the angular rotation of said rotor according to the relationship:

(Sin R sin a+tan P cos a) and (tan P sin a+sin R cos a) a fifth potentiometer energized by said second potentiometer output voltage and having a moving contact arm providing an output voltage proportional to the sine of its motion, a sixth potentiometer energized by said fourth potentiometer output voltage and having a moving contact arm providing an output voltage proportional to the tangent of its motion, motor means responsive to the difierence between the resultant output potentials of said two-phase rotary transformer and the output potentials of said fifth and sixth potentiometers to drive the moving contact arms of said fifth and sixth potentiometers to reduce any voltage difference to zero, whereby the amount of motion imparted to the contact arms of said fifth and sixth potentiometcrs represents level and cross-level angular motion in accordance with the relationships:

Sec P sin L= sin R sin a+tan P cos a cos R tan Z=tan P sin a+sin R cos a 6. A computer for the simultaneous solution of equations in the form:

Sec P sin L= sin R sin a+tan P cos oc Cos R tan Z=tan P sin a+sin R cos a comprising, a first source of alternating voltage, a first potentiometer connected across said first source, the slider contact of said first potentiometer being adapted to move such that the voltage tapped off is proportional to sin R, a second source of alternating voltage, a second potentiometer connected across said second source, the slider contact of said second potentiometer being adapted to move such that the voltage tapped off is proportional to tan P, a resolver, whose variable angle between rotors and stators is designated as a, said resolver being adapted to receive said voltages proportional to sin R and tan P and to produce resultant output voltages proportional to (sin R sin a-i-tan P cos a) and (tan P sin +sin R cos a) a third source of alternating voltage, a third potentiometer connected across said third source, the slider contact of said third potentiometer being adapted to move such that the voltage tapped off is proportional to see P, a fourth source of alternating voltage, a fourth potentiometer connected across said fourth source, the slider contact of said fourth potentiometer being adapted to move such that the voltage tapped off is proportional to cos R, a fifth potentiometer adapted to receive across it said voltage proportional to sec P, the slider contact of said fifth potentiometer being adapted to move such that the balancing voltage tapped oif is proportional to (sec P sin L), a sixth potentiometer adapted to receive across it said voltage proportional to cos R, the slider contact of said sixth potentiometer being adapted to move such that the balancing voltage tapped off is proportional to (cos R tan Z), a first follow-up motor means responsive to said resolver output voltage proportional to (sin R sin a+tan P cos a) and the balancing voltage derived from said fifth potentiometer and mechanically coupled to said slider contact of said fifth potentiometer for moving said slider contact to reduce the difierence between said resolver output voltage and said balancing voltage from said fifth potentiometer to zero, and a second follow-up motor means responsive to said resolver output voltage proportional to (tan P sin u+sin R cos a) and the balancing voltage output derived from said sixth potentiometer and mechanically coupled to said slider contact of said sixth potentiometer for moving said slider contact to reduce the difference between said resolver output voltage and said balancing voltage of said sixth potentiometer to zero, whereby the displacement of said slider contacts of said fifth and sixth potentiometers are proportional to the quantities L and Z, respectively.

References Cited in the file of this patent UNITED STATES PATENTS 798,236 Usener Aug. 29, 1905 2,080,186 Reymond May 11, 1937 2,390,374 Jorden Dec. 4, 1945 2,404,387 Lovell July 23, 1946 2,417,229 Alexanderson Mar. 11, 1947 2,463,687 Gittens Mar. 8, 1949 

